We have to ask ourselves what a memory means. Is a tattoo with a motto a memory? It might affect behavior. Is immunity memory? That's not in the brain. If you exercise hard and get big muscles is that memory? Are epigenetic changes memory? Is adaption of hormonal glands (shrinking balls from injecting testo) which affect behavior memory? I'd argue we are full of memory.
if anyone else wondered, it is of course pseudoscience that hearts have neurons, they have cardiomyocytes which are quite different than neurons. But its easy to understand why thats a another fantasy spread by popular "science" journalism (add it to the list of bullshit they spread lol).
All major organs have neurons, or at the very least project axon "fibers" (but the heart specifically has full nerve bundles).
They make up the autonomic nervous system, which is the network of motor and sensor neurons connected to the central nervous system (brain and spinal cord). The latter does your thinking, the former keeps you from suffocating.
I'm not sure I understand the distinction you're making, and whether the nerves are considered part of the heart there are most definitely nerves into the heart. From [1],
"The vagus nerve directly innervates the sinoatrial node; when activated, it serves to lower the heart rate". This is illustrated here [2], in a diagram from Gray's Anatomy of the Human Body.
I'm not up to date on heart anatomy, though. As I recall, it's true that cardiomycytes also perform some neuron-like functions, but wasn't there a "pulse clock" bundle that's made up of neurons? Or are those still cardiomycytes?
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Seems like there might be some interesting experiments exploring the memory/instinct boundary?